Seminars

Asymptotic order-of-vanishing functions on the pseudoeffective cone

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2016-12-12
15:30:00 - 18:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)



Let v be a discrete valuation on the function field of a normal projective > variety X. Ein, Lazarsfeld, Mustata, Nakamaye, and Popa showed that v induces a > nonnegatively-real-valued continuous function on the big cone of X, which they called > the asymptotic order of vanishing along v. The case where v is given by the order of > vanishing along a prime divisor was studied earlier by Nakayama, who extended the domain > of the function to the pseudoeffective cone and investigated the continuity of the > extended function. I will explain how Nakayama's results can be generalized to any > discrete valuation v, using an approach inspired by Lazarsfeld and Mustata's > construction of the global Okounkov body, which has a quite different flavor from the > arguments employed by Nakayama. A corollary is that the asymptotic order-of-vanishing > function can be extended continuously to the pseudoeffective cone of X if the cone is > polyhedral.